Reference Dependence Lecture 2

Mark Dean

Princeton University - Behavioral Economics

The Story So Far

� De�ned reference dependent behavior� Additional argument in the choice function/preferences

� Provided evidence for reference dependent behavior� Change in risk attitudes� Endowment e¤ect� Status quo bias

� Introduce the �Standard Model�of reference dependentbehavior

� Prospect Theory

Plan for Today

� Prospect theory for riskless choice� Alternative models of reference dependent preferences

� Koszegi and Rabin [2006, 2007]

Prospect Theory for Riskless Choice

� Extended to Riskless choice by assuming that objects ofchoice have a number of dimensions

� if x � y when reference point is s, then x � y when referencepoint is r

An Extreme Case

� Assume that utility is additively separable, so utility offx1, x2g from reference point r1, r2 is given by

V1(x1 � r1) + V2(x2 � r2)

where

Vi (y) = Ui (y) for y � 0= �λUi (�y) for y � 0

for λ > 1

Can This Explain Status Quo Bias?

� Yes: consider a good to be a bundle fp, cg of pens andchocolate bars

� When reference point is f1, 0g then utility of f1, 0g andf0, 1g are

0 and � λU1(1) + U2(1)

� Whereas, when the reference point is f0, 1g the respectiveutilities are

U1(1)� λU2(1) and 0

� Clearly it is possible for 0 > �λU1(1) + U2(1) andU1(1)� λU2(1) < 0

� Also, if U1(1)� λU2(1) > 0 then 0 > �λU1(1)� U2(1), soif f1, 0g is chosen when it is not the status quo will de�nitelybe chosen when it is the status quo

WTP/WTA Gap

� Assume initially endowed with good of utility u, and �ndPWTA, PWTP such that

0 = PWTA � λu

u � λPWTP = 0

� ImpliesPWTAPWTP

= λ2

Is there Really An Endowment E¤ect

� Plott and Zellner [2005] argue that WTP/WTA gap may bedue to subject misconceptions

� While most papers control for some sources of misconception,none control for all of them

� Incentive compatible elicitation mechanism� Training on the properties of the mechanism� Paid Practice rounds� Anonymity

Is there Really An Endowment E¤ect

Does Market Experience Remove the Endowment E¤ect

A Model of Reference Dependent Preferences

� Koszegi and Rabin [2006, 2007] introduce a new model ofreference dependent preferences

� Two main developments1 Allow for �consumption utility�as well as �gain loss�utility2 Allows for stochastic reference points3 Generates reference point endogenously through �personalequilibrium�

� Warning - not liked by decision theorists� If we do not see dimensions, utilities, then no empirical content� See "The Case for Mindless Economics" by Gul andPesendorfer

Set Up

� Let c be a consumption bundle and r be a reference point� Each are m dimensional vectors

c =

8><>:c1...cm

9>=>; , r =8><>:r1...rm

9>=>;� If c and r are know with certainty, then utility is given byu(c jr)

� If c and r are distributed according to F and G , then U(F jG )is given by Z Z

u(c jr)dG (r)dF (c)

Set Up

� Assume that utility is separable across dimensions, then

u(c jr) = ∑k

mk (ck ) + nk (ck jrk )

where

� mk (.) is the consumption utility along dimension k� nk (ck jrk ) = µ(mk (ck )�mk (rk )) is �universal gain lossfunction�

Assumptions about Gain Loss Function

� µ assumed to have the following properties

� Continuous, twice di¤erentiable away from 0, and µ(0) = 0� Strictly increasing� (Loss aversion 1) y > x > 0 implies that

µ(y) + µ(�y) < µ(x) + µ(�x)

� (Loss aversion 2)

limx!0 µ0(�jx j)limx!0 µ0(jx j) = λ > 1

� (Diminishing Sensitivity) µ00(x) � 0 for x > 0 and µ00(x) � 0for x < 0

Implications

1 For all F ,G ,G 0 such that the marginals of G 0 FOSD themarginals of G in each dimension, U(F jG ) � U(F ,G 0)

2 For any c 6= c 0, u(c jc 0) � u(c 0jc 0)) u(c jc) > u(c 0jc)3 If µ is piecewise linear then

U(F jF 0) � U(F 0jF 0)) U(F jF ) > U(F 0jF )

Personal Equilibrium

� Where does reference point come from?� KR suggest that it should be expectations over outcomes� Where do expection come from?� One extreme assumption: rational expectations

� Let x be your reference point� Then x must be optimal choice given reference point x

� In other words, a reference point must be consistent

Personal Equilibrium

� Let Q be a distribution over possible choice sets

� e.g. Q is a probability distribution over prices� Let Dl be the choice set available when price is l

� A choice function fFl ,Dlgl2R is a personal equilibrium if, forevery l

Fl =Zmaxc2D

U(c jFl )dQl

An Example of Shopping

� Two dimensions:� c1 2 f0, 1g whether shoes have been purchased� c2 2 R dollar wealth

� Assume m(c) = c1 + c2� Assume µ(x) = µx in gain domain λµx in the loss domain

An Example of Shopping

λ

� If expecting to buy, then

1� p > �λµ+ µp

assuming

p � pmin =(1+ λµ)

(1+ µ)

� If not expecting to buy then

0 > 1+ µ� (1+ µλ)p

assuming

p � pmax =(1+ µ)

(1+ λµ)

� So between these two prices, two personal equilibriadepending on expectations

Price Uncertainty

� Imagine expecting price pl < pmin with probability ql andph > pmax with probability qh

� What would happen at intermediate price pm?� Utility of buying is

1� pm+qh(µ� µλpm)

+ql (pm � pl )

� The utility from not buying is

ql (�µλ+ µpl )

Special Case

� PL = 0: Buy if and only if

pm < 1� (1� ql )µ(λ� 1)1+ µλ

Increasing in ql� pl � 0 and ql = 1

pm < 1+ plµ(λ� 1)1+ µλ

Increasing in pl

Endowment E¤ect for Risk

� One implication of stochastic reference point: EndowmentE¤ect for risk

� People should be less risk averse when reference point isstochastic

� See Koszegi and Rabin [2007] for theory� See Sprenger [2012] for evidence